Pandas Profiling Report

Dataset statistics

Number of variables	9
Number of observations	500
Missing cells	40
Missing cells (%)	0.9%
Duplicate rows	0
Duplicate rows (%)	0.0%
Total size in memory	35.3 KiB
Average record size in memory	72.3 B

Variable types

NUM	8
BOOL	1

Warnings

`GRE Score` has 15 (3.0%) missing values	Missing
`TOEFL Score` has 10 (2.0%) missing values	Missing
`University Rating` has 15 (3.0%) missing values	Missing
`Serial No.` has unique values	Unique

Reproduction

Analysis started	2022-10-14 10:38:33.919061
Analysis finished	2022-10-14 10:38:44.815211
Duration	10.9 seconds
Software version	pandas-profiling v2.9.0
Download configuration	config.yaml

Serial No.
Real number (ℝ_≥0)

UNIQUE

Distinct	500
Distinct (%)	100.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	250.5
Minimum	1
Maximum	500
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	1
5-th percentile	25.95
Q1	125.75
median	250.5
Q3	375.25
95-th percentile	475.05
Maximum	500
Range	499
Interquartile range (IQR)	249.5

Descriptive statistics

Standard deviation	144.4818328
Coefficient of variation (CV)	0.5767737835
Kurtosis	-1.2
Mean	250.5
Median Absolute Deviation (MAD)	125
Skewness	0
Sum	125250
Variance	20875
Monotocity	Strictly increasing

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
500	1	0.2%
171	1	0.2%
158	1	0.2%
159	1	0.2%
160	1	0.2%
161	1	0.2%
162	1	0.2%
163	1	0.2%
164	1	0.2%
165	1	0.2%
Other values (490)	490	98.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	1	0.2%
2	1	0.2%
3	1	0.2%
4	1	0.2%
5	1	0.2%

Value	Count	Frequency (%)
500	1	0.2%
499	1	0.2%
498	1	0.2%
497	1	0.2%
496	1	0.2%

GRE Score
Real number (ℝ_≥0)

MISSING

Distinct	49
Distinct (%)	10.1%
Missing	15
Missing (%)	3.0%
Infinite	0
Infinite (%)	0.0%

Mean	316.5587629
Minimum	290
Maximum	340
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	290
5-th percentile	298
Q1	308
median	317
Q3	325
95-th percentile	335
Maximum	340
Range	50
Interquartile range (IQR)	17

Descriptive statistics

Standard deviation	11.2747043
Coefficient of variation (CV)	0.03561646565
Kurtosis	-0.6844666911
Mean	316.5587629
Median Absolute Deviation (MAD)	8
Skewness	-0.05168658259
Sum	153531
Variance	127.1189571
Monotocity	Not monotonic

Histogram with fixed size bins (bins=49)

Value	Count	Frequency (%)
324	22	4.4%
312	22	4.4%
321	17	3.4%
316	17	3.4%
327	17	3.4%
322	17	3.4%
314	16	3.2%
320	16	3.2%
311	16	3.2%
317	15	3.0%
Other values (39)	310	62.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
290	2	0.4%
293	1	0.2%
294	2	0.4%
295	5	1.0%
296	5	1.0%

Value	Count	Frequency (%)
340	9	1.8%
339	3	0.6%
338	4	0.8%
337	2	0.4%
336	5	1.0%

TOEFL Score
Real number (ℝ_≥0)

MISSING

Distinct	29
Distinct (%)	5.9%
Missing	10
Missing (%)	2.0%
Infinite	0
Infinite (%)	0.0%

Mean	107.1877551
Minimum	92
Maximum	120
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	92
5-th percentile	98
Q1	103
median	107
Q3	112
95-th percentile	118
Maximum	120
Range	28
Interquartile range (IQR)	9

Descriptive statistics

Standard deviation	6.112899387
Coefficient of variation (CV)	0.0570298294
Kurtosis	-0.6645653663
Mean	107.1877551
Median Absolute Deviation (MAD)	5
Skewness	0.1020677321
Sum	52522
Variance	37.36753892
Monotocity	Not monotonic

Histogram with fixed size bins (bins=29)

Value	Count	Frequency (%)
110	42	8.4%
105	37	7.4%
104	29	5.8%
107	28	5.6%
112	27	5.4%
106	26	5.2%
103	25	5.0%
102	24	4.8%
100	24	4.8%
99	22	4.4%
Other values (19)	206	41.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
92	1	0.2%
93	2	0.4%
94	2	0.4%
95	3	0.6%
96	6	1.2%

Value	Count	Frequency (%)
120	9	1.8%
119	10	2.0%
118	10	2.0%
117	8	1.6%
116	16	3.2%

University Rating
Real number (ℝ_≥0)

MISSING

Distinct	5
Distinct (%)	1.0%
Missing	15
Missing (%)	3.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.121649485
Minimum	1
Maximum	5
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	2
median	3
Q3	4
95-th percentile	5
Maximum	5
Range	4
Interquartile range (IQR)	2

Descriptive statistics

Standard deviation	1.146160209
Coefficient of variation (CV)	0.3671649281
Kurtosis	-0.8340454487
Mean	3.121649485
Median Absolute Deviation (MAD)	1
Skewness	0.0910567357
Sum	1514
Variance	1.313683224
Monotocity	Not monotonic

Histogram with fixed size bins (bins=5)

Value	Count	Frequency (%)
3	154	30.8%
2	124	24.8%
4	103	20.6%
5	72	14.4%
1	32	6.4%
(Missing)	15	3.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	32	6.4%
2	124	24.8%
3	154	30.8%
4	103	20.6%
5	72	14.4%

Value	Count	Frequency (%)
5	72	14.4%
4	103	20.6%
3	154	30.8%
2	124	24.8%
1	32	6.4%

SOP
Real number (ℝ_≥0)

Distinct	9
Distinct (%)	1.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.374
Minimum	1
Maximum	5
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	1
5-th percentile	1.5
Q1	2.5
median	3.5
Q3	4
95-th percentile	5
Maximum	5
Range	4
Interquartile range (IQR)	1.5

Descriptive statistics

Standard deviation	0.9910036208
Coefficient of variation (CV)	0.2937177299
Kurtosis	-0.7057169536
Mean	3.374
Median Absolute Deviation (MAD)	0.5
Skewness	-0.2289723963
Sum	1687
Variance	0.9820881764
Monotocity	Not monotonic

Histogram with fixed size bins (bins=9)

Value	Count	Frequency (%)
4	89	17.8%
3.5	88	17.6%
3	80	16.0%
2.5	64	12.8%
4.5	63	12.6%
2	43	8.6%
5	42	8.4%
1.5	25	5.0%
1	6	1.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	6	1.2%
1.5	25	5.0%
2	43	8.6%
2.5	64	12.8%
3	80	16.0%

Value	Count	Frequency (%)
5	42	8.4%
4.5	63	12.6%
4	89	17.8%
3.5	88	17.6%
3	80	16.0%

LOR
Real number (ℝ_≥0)

Distinct	9
Distinct (%)	1.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.484
Minimum	1
Maximum	5
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	1
5-th percentile	2
Q1	3
median	3.5
Q3	4
95-th percentile	5
Maximum	5
Range	4
Interquartile range (IQR)	1

Descriptive statistics

Standard deviation	0.9254495739
Coefficient of variation (CV)	0.2656284655
Kurtosis	-0.7457485106
Mean	3.484
Median Absolute Deviation (MAD)	0.5
Skewness	-0.1452903146
Sum	1742
Variance	0.8564569138
Monotocity	Not monotonic

Histogram with fixed size bins (bins=9)

Value	Count	Frequency (%)
3	99	19.8%
4	94	18.8%
3.5	86	17.2%
4.5	63	12.6%
5	50	10.0%
2.5	50	10.0%
2	46	9.2%
1.5	11	2.2%
1	1	0.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	1	0.2%
1.5	11	2.2%
2	46	9.2%
2.5	50	10.0%
3	99	19.8%

Value	Count	Frequency (%)
5	50	10.0%
4.5	63	12.6%
4	94	18.8%
3.5	86	17.2%
3	99	19.8%

CGPA
Real number (ℝ_≥0)

Distinct	184
Distinct (%)	36.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	8.57644
Minimum	6.8
Maximum	9.92
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	6.8
5-th percentile	7.638
Q1	8.1275
median	8.56
Q3	9.04
95-th percentile	9.6
Maximum	9.92
Range	3.12
Interquartile range (IQR)	0.9125

Descriptive statistics

Standard deviation	0.6048128003
Coefficient of variation (CV)	0.07052026253
Kurtosis	-0.5612783981
Mean	8.57644
Median Absolute Deviation (MAD)	0.46
Skewness	-0.02661251732
Sum	4288.22
Variance	0.3657985234
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
8	9	1.8%
8.76	9	1.8%
8.54	7	1.4%
8.45	7	1.4%
8.56	7	1.4%
8.12	7	1.4%
7.88	6	1.2%
8.64	6	1.2%
8.66	6	1.2%
9.11	6	1.2%
Other values (174)	430	86.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
6.8	1	0.2%
7.2	1	0.2%
7.21	1	0.2%
7.23	1	0.2%
7.25	1	0.2%

Value	Count	Frequency (%)
9.92	1	0.2%
9.91	1	0.2%
9.87	2	0.4%
9.86	1	0.2%
9.82	1	0.2%

Research
Boolean

Distinct	2
Distinct (%)	0.4%
Missing	0
Missing (%)	0.0%
Memory size	3.9 KiB

1	280
0	220

Common Values
Chart

Value	Count	Frequency (%)
1	280	56.0%
0	220	44.0%

Chance of Admit
Real number (ℝ_≥0)

Distinct	61
Distinct (%)	12.2%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.72174
Minimum	0.34
Maximum	0.97
Zeros	0
Zeros (%)	0.0%
Memory size	3.9 KiB

Quantile statistics

Minimum	0.34
5-th percentile	0.47
Q1	0.63
median	0.72
Q3	0.82
95-th percentile	0.94
Maximum	0.97
Range	0.63
Interquartile range (IQR)	0.19

Descriptive statistics

Standard deviation	0.141140404
Coefficient of variation (CV)	0.1955557458
Kurtosis	-0.4546817998
Mean	0.72174
Median Absolute Deviation (MAD)	0.1
Skewness	-0.28996621
Sum	360.87
Variance	0.01992061363
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.71	23	4.6%
0.64	19	3.8%
0.73	18	3.6%
0.72	16	3.2%
0.79	16	3.2%
0.78	15	3.0%
0.76	14	2.8%
0.8	13	2.6%
0.7	13	2.6%
0.94	13	2.6%
Other values (51)	340	68.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.34	2	0.4%
0.36	2	0.4%
0.37	1	0.2%
0.38	2	0.4%
0.39	1	0.2%

Value	Count	Frequency (%)
0.97	4	0.8%
0.96	8	1.6%
0.95	5	1.0%
0.94	13	2.6%
0.93	12	2.4%

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

First rows

	Serial No.	GRE Score	TOEFL Score	University Rating	SOP	LOR	CGPA	Research	Chance of Admit
0	1	337.0	118.0	4.0	4.5	4.5	9.65	1	0.92
1	2	324.0	107.0	4.0	4.0	4.5	8.87	1	0.76
2	3	NaN	104.0	3.0	3.0	3.5	8.00	1	0.72
3	4	322.0	110.0	3.0	3.5	2.5	8.67	1	0.80
4	5	314.0	103.0	2.0	2.0	3.0	8.21	0	0.65
5	6	330.0	115.0	5.0	4.5	3.0	9.34	1	0.90
6	7	321.0	109.0	NaN	3.0	4.0	8.20	1	0.75
7	8	308.0	101.0	2.0	3.0	4.0	7.90	0	0.68
8	9	302.0	102.0	1.0	2.0	1.5	8.00	0	0.50
9	10	323.0	108.0	3.0	3.5	3.0	8.60	0	0.45

Last rows

	Serial No.	GRE Score	TOEFL Score	University Rating	SOP	LOR	CGPA	Research	Chance of Admit
490	491	307.0	105.0	2.0	2.5	4.5	8.12	1	0.67
491	492	297.0	99.0	4.0	3.0	3.5	7.81	0	0.54
492	493	298.0	101.0	4.0	2.5	4.5	7.69	1	0.53
493	494	300.0	95.0	2.0	3.0	1.5	8.22	1	0.62
494	495	301.0	99.0	3.0	2.5	2.0	8.45	1	0.68
495	496	332.0	108.0	5.0	4.5	4.0	9.02	1	0.87
496	497	337.0	117.0	5.0	5.0	5.0	9.87	1	0.96
497	498	330.0	120.0	5.0	4.5	5.0	9.56	1	0.93
498	499	312.0	103.0	4.0	4.0	5.0	8.43	0	0.73
499	500	327.0	113.0	4.0	4.5	4.5	9.04	0	0.84

Overview

Variables

Interactions

Correlations

Pearson's r

Spearman's ρ

Kendall's τ

Phik (φk)

Missing values

Sample

First rows

Last rows